I have now learned about three different versions of the 12 basic striking angles in Kali. Apparently there are hundreds - as many as there are different systems of it and they range from familiar to way out there. Have any of you escrimadors(?) found a particular system or subsystem that you find more effective than others? Or just that you particularly like? I've found that 1 thru 5 are pretty universal, with some odd variations out there, but 6 thru 12 seem like they're anyone's guess. Would love to hear it!

Its almost impossible to do this remotely, without being able to stand and show you...

From modern arnis and arnis mati:

1-4 are head/shoulder + elbows alternating both sides
5 is a thrust to the stomach.
6 + 7 are inverted thrusts to the chest cavity, both sides
8 + 9 are strikes to take the legs out, both sides
10 + 11 are inverted thrusts to the eyes, both sides
12 is on the top of the head.

I've seen other variations but these seem to flow really nicely.

Note: 1-4 are diagonal cuts through the torso, not just simple cuts on the side.

Yes, I practice 1-5 identically. It's not hard to visualize these btw since I'm familiar with them. The major differences I've learned are 6 and 7 go to the chin and nose/eyes and 10 and 11 are overhead backswings (can't remember the name of this strike!) to the sides of the head/temples.
The garimot system I posted about is entirely different - angles 1 and 3 / 2 and 4 become one contiuous flowing strike. IE, you start a common 1 swing from shoulder level, across and down to the opposite hip, but then rip it back, only this time point the stick (again at shoulder level) directly at your opponent. This messes with their depth perception as they can't see how close the stick is to them easily and opens the doors for some serious offenses. Works wonders with the knife too.

forgot lucky #13? (up into the groin)

How about:
1/2 - forehand/backhand to the head
3/4 - forehand/backhand to the ribs/elbow level
5/6 - forehand/backhand to the legs
7/8 - forehand/backhand slashing up
9/10 - Abaniko to the head
11 - top of the head
12 - thrust to the abdomen/chest
13 - (refer to top of post)

*not including Punyo strikes or disarms

That's a new one to me. I like it!

The majority of systems seem to have either 5 or 12 angles. The only common thing I've seen is that #1 is normally a forehand attack to the head. It can be diagonal (as in Doce Pares, Balintawak, Lameco, Inosanto kali, Modern Arnis, Rapid Arnis...) but some systems, notably Pekiti Tirsia, have it as a horizontal shot.

Sometimes you learn new sets of angles within a system (Some Doce Pares groups have angles for long range, close range and knife). I trained in one arnis style that started with 5 angles, then 8, then 12, then 20. Also systems that are composed of several styles have different sets of angles. I have seen at least 4 sets of angles taught by Dan Inosanto during seminars (over a 15 year+ period).

That said the first style I trained in, although descended for Doce Pares, had 7 angles. (Standard first 4 - forehand to head, backhand to head, forehand to body, backhand to body - then a straight thrust, palm-up thrust and palm down thrust)